MCh 7 Consumption_new

Ch7 Consumption Consumption and investment are important to both growth and fluctuations. With regard to growth, the division of society’s resources between consumption and various types of investment - in physical capital, human capital, and R&D- is central to standards of living in the long run. That division is determined by the interaction of households’ allocation of their incomes between consumption and saving given the rates of return and other constraints they face, and firms’ investment demand given the interest rates and other constraints they face. With regard to fluctuations, Consumption and investment are the major components of aggregate demand. Two reasons of studying consumption and investment: firstly, they are also the main channels through which government policy and financial markets influence the macro-economy, and have important feedback effects on financial markets. Second, much of the most insightful empirical work in macroeconomics over the past 25 years has been concerned with consumption and investment. 7.1 Consumption Under Certainty：The Life-Cycle/Permanent Income Hypothesis Modigliani and Brumberg, 1954; Friedman, 1957 The basic insight of the Permanent Income and Life Cycle theories of consumption is straightforward. Consider an individual who wishes to maximise utility by choosing consumption in each period of their life. Further suppose that the rates of time preference and interest are zero and that the path of future income is known. In this simple case optimality requires that the marginal utility of consumption is constant across periods. If this were not true a reallocation of a unit of consumption from a period in which the marginal utility is low to one which it is high will increase total utility. It follows that any path along which the marginal utility is not constant cannot be equilibrium. Since the marginal utility is constant so too is the level of consumption. That is to maximise utility individual smooth consumption. 1. The model Assumptioans: Consider an individual who lives for T periods who maximize lifetime utility EMBED Equation.3 >0 <0 s.t. EMBED Equation.3 EMBED Equation.3 Assume: (1) The individual can save and borrow at ! (2) ; (3) Certainty. Behavior: Lagrangian: L = F.O.C: Then: With the budget constraint yields for all t Implications: (1) The individual divides his or her life resources equally among each period of life. (2) Friedman (1957): Permanent income: Transitory income: A temporary tax cut may have little impact on consumption. And the time pattern of income is not important to consumption, it is critical to saving. (3) current income＞permanent income: saving current income＜permanent income: borrowing What is saving? Here, saving is only future consumption! Saving motives, preferences between present and future consumption, information about future consumption prospects. 2. Empirical Application: Understanding Estimated Consumption Functions Keynesian Consumption Function (1936) (1) Across households at a point in time, the relationship is indeed of the type that keynes postitued. F7.1(a); (2) But within a country over time, aggregate consumption is essentially proportional to aggregate income. F7.1(b); (3) The slope of the estimated consumption function is similar for blacks and whites, but the intercept is higher for whites. F7.1(c). Friedman’s (1957) permanent income hypothesis provides a straightforward explanation of all these findings. Suppose that consumption is in fact: , , Consider the regression: Implications: an increase in current income is associated with an increase in consumption only to the extent that it reflects an increase in permanent income. When the variation in permanent income is much greater than the variation in transitory income, almost all differences in current income reflect differences in permanent income, thus consumption rises nearly one for one with current income. But when the variation in permanent income is small relative to the variation in transitory income, little of the variation in current income comes from variation in permanent income, and so consumption rises little with current income. This analysis can be used to understand the estimated consumption in F7.1: (1) Across households at a point in time, the relationship is indeed of the type that keynes postitued. F7.1(a): , and substantially less than 1: smaller since households are only at different points in there life cycles. (2) But within a country over time, aggregate consumption is essentially proportional to aggregate income. F7.1(b): Almost all the variation in aggregate income reflects long-run growth, that is, permanent increases in the economy’s resources. Thus, larger, and , . (3) The slope of the estimated consumption function is similar for blacks and whites, but the intercept is higher for whites. F7.1(c): The relative variances of permanent and transitory income are similar in the two groups, and . But blacks’ average incomes are lower than whites’, as a result, . 7.2 Consumption under Uncertainty: The Random-Walk Hypothesis Individual Behavior (Hall, 1978) We extend our analysis to acount for uncertainty. Continue to assume that both interest rate and discount rate are zero. In additon, suppose that the instantaneous utility function is quadratic. Thus the individual maximizes (1) Quadratic utility is the source of certainty-equivalence(marginal utility is linear) The expected lifetime budget constraint is, (2) Euler Equation: for In the case of Quadratic utility for (4) That is for The expected level of consumption is equal across all periods. Since the expected level of consumption is constant across periods and for maximisation the budget constraint holds with equality we have that, (5) Or simply, (6) The individual consumes of their lifetime resources in each period of their lives. Individual saving in any period is equal to income minus consumption so that using (6) expected saving is equal to, (7) Variations in current income about the mean level result in variations in current saving rather than in current consumption. The individual uses saving and borrowing to smooth the path of consumption. Clearly saving is really future consumption. In any one period of time there is likely to be two types of income. There is an average component or permanent income, which is lifetime income divided by the expected lifetime, and there are fluctuations about the mean or transitory income. Permanent income determines consumption in any given period, transitory income determines saving. The distinction has important implications for policy because it implies that the strength of any policy change to stimulate income depends upon how good the change is at increasing the level of permanent income. Implications · A Random Walk The first order conditions imply that the expected level of next period consumption is equal to this period’s consumption. By definition the actual level of consumption equals that expected one period ago plus some stochastic element. That is, (8) Where we have used the first order condition. Consumption should follow a random walk because if consumption is expected to change one can do a better job of smoothing. This implies that a forecast of future consumption based on current consumption cannot be improved upon. This has spawned a lot of important empirical research. · What Determines the Change in Consumption e. Consider for concreteness the change from period 1 to period 2 The change in the individual’s estimate of his or her life-time resources divided by the number of periods of life remaining. 7.3 Empirical Application: Two Tests of the Random Walk Hypothesis 1. Campbell and Mankiw’s Test Using Aggregate Data (1989b) Some fraction of consumers simply spends their current income, and the remainder behaves as the random walk theory Where is the change in consumers’ estimate of their permanent income from t-1 to t. (1) and are almost surely correlated. Times when income increases are usually also times when households receive favourable news about their total life-time incomes. This means that the right hand side variable is positively correlated with the error term. Thus estimating by OLS leads to estimates of that are biased upward. (2) Use instrumental variables (IV) rather than OLS. The intuition behind IV estimation is easiest to see using the TSLS interpretation of instrumental variables. (a) First choose IV variables correlated with the right hand side variables but uncorrelated with the residual, the first stage regression is a regression of the right hand side variable on the instruments. (b) The second stage regression is then a regression of the left hand side variable, on the fitted value of from the first stage regression, . That is consists of two terms and . By assumption the instrument used to construct are not systematically correlated with . And since is the fitted value from a regression, by construction, it is uncorrelated with the residual from that regression . Thus and are uncorrelated, and regressing on yields a valid (see the notes: consistent but not unbiased) estimate ofλ. Campbell and Mankiw’s test result: Consumption as real purchases of consumer nondurables and services per person Income as real disposable income per person Quarterly data from 1953-1986 Various sets of instruments: a base case: With i =3,λ= 0.42 (s.e 0.16) With i =5,λ= 0.52 (s.e 0.13) λstatistically significant but far less than 1. Thus RW of C rejected and the permanent income Hypothesis is also important. 2. Shea’s Test Using Household Data (1995) Disadvantages Using Aggregate Data: The number of observations is small. Difficult to find variables with much predicative power for changes in income [IV]. The theory concerns individuals’consumption, and additional assumptions are needed for the predictions of the model to aggregate data. Shea (1995) (1) Wage earners covered by long term union contract: PSID data ↓predictive power to changes in earnings 0.86 (se 0.20) (2) λ=0.89 (se 0.46), departure from RW of consumptions. Liquidity constraints? Shea’s tests for liquidity constraints in two ways: ①Follow Zeldes(1989) etc: Households with and without liquid assets. Households with liquid assets can smooth their consumption by running down these assets rather than borrowing. Thus if liquidity constraints are the reason that predictable wage changes affect consumption growth, the prediction of PIH will fail only among the households with no assets. Shea finds, however, that the estimated effect of expected wage groth on comsumption is essentially the same in the two groups. Thus liquidity constraints are not the reason! ②Follow Altonji and Siow(1987): split the low wealth sample according to whether the expected change in the real wage is positive or negative. Individuals facing expected declines in income need to save rather than borrow to smooth their consumption. If liquidity constraints are important, predictable wage increase produce predictable consumption increases, but predictable wage decreases do not produce predictable consumption decreases. Shea;s findings are the opposite of this. Thus liquidity constraints are not the reason! 3. Discusson: Conformative researches of the above findings: Shapiro and Slemrod (1995), Parker (1999), Souleles (1999) identify features of government policy that cause predictable income movements. This pattern appears to break down, however, shen the predictable movements in income are large and regular (Paxson, 1993; Browning and Collado, 2001, and Hsieh, 2003). The permanent income hypothesis describes consumption behaviour well. 7.4 The Interest Rate and Saving An important issue is how saving and consumption responds to changes in the interest rate. As the Diamond model allowing for a non-zero rate of interest and a positive discount rate leads to an Euler equation of the form. (8) Euler equation: Solving this is in the usual way yields, (9) If , then consumption increases over time. The extent of this increase depends upon the elasticity of substitution. In addition fluctuations in will lead to fluctuations in the predictable component of consumption growth. Mankiv (1981), hansen and Singleton (1983), Hall (1988b), Compbell and Mankiv(1989b) and others examine how much consumption growth responds to variations in the real interest rate. The Interste Rate and Saving in the Two Period Case Although an increase in causes the path of consumption to more steeply sloped, it does not necessarily follow that the increase reduces initial consumption and thereby raises saving. The complication is that the change in has not only a substitution effect, but also an income effect. Specifically, if the individual is a net saver, the increase in allows him or her to attain a higher path of consumption than before. Possibilities for the income effect and current consumption The above assumes the individual is a net saver but it is also clearly possible that the ind ividual is a net borrower. Assume: no initial wealth, and Slope= : to give 1 unit of first period consumption allows the individual to increase second period consumption by . And the budget line become steeper. Substitution effect and income effect. Saver (most possible at macro-level) No saver no borrower: no income effect Borrower Fig 7.2 The interest rate and consumption choices in the two-period cases The maximum possible level of second period consumption increases but the maximum amount of first period consumption, financed by borrowing against second period income falls. The extent of any income effect depends upon whether or not the individual is a net saver prior to the increase in the interest rate. ①Suppose that before the interest rate change net saving is zero so that the indifference curve is tangent to the budget constraint at . Since net saving is zero the income effect is zero and so consumption in period 1 must fall. That is if net saving is zero the interest rate has no effect on returns and this leaves only the substitution effect so the new point of tangency is above and to the left. ② If the initial point of tangency is above and to the left of first period consumption is less than first period income and the individual is a net saver. In this case the increase in the interest rate has a positive income effect and the point of tangency on the new budget constraint could be above and to the right of the previous point. That is since the individual is better off he/she can raise both first and second period consumption. , The income effect and substitution effect only work in opposite directions if net aggregate saving is positive and the income effect is positive. The overall effect is ambiguous; in this case, saving does not change. ③ Finally there is also the possibility that the initial point of tangency is to right of so the first period consumption exceeds first period income. An increase in the interest rate reduces the income of net borrowers and so reduces first period consumption. ④ At the macroeconomic level the stock of net wealth is positive and so the flow of saving must be on average positive and the income effect is positive. An increase in the interest rate thus hase two competing effects, and the overall effect is ambiguous.This also reduces the effectiveness of a cut in interest rates on consumption and aggregate demand. ⑤ complications and extensions. Problem 7.5; Summers (1981a); Carroll(1997) . Unless the elasticity of substitution between consumption in different periods is large, increases in the interest rate are unlikely to bring about substantial increases in saving. This conclusion is limited for two reasons: Other changes such as tax. Eg. taxes on interest income and other taxes that leaves government revenue unchanged have only a substitution effect. If individuals have long horizons, small changes in saving can accumulate over time into large changes in wealth (Summers, 1981a). however, the presence of uncertainty weakens this conclusion (Carroll, 1997). 7.5 Consumption and Risky Assets Individuals can invest in different types of assets, almost all of which have uncertain returns. Allowing for different types of assets with uncertainty modifies the first order condition of the previous example, and raises new issues concerning both household behaviour and asset markets. The Conditions for Individual Optimization Euler equation: (1) Where is the return on asset . or: (2) With Quadratic utility as above, (3) · The striking result is that the overall risk associated with asset does not affect the demand for that asset. Intuitively, a marginal increase in holdings of an asset that is risky, but whose risk is not correlated with the overall risk the individual faces, does not increase the variance of the individual’s consumption. Thus in evaluation that marginal decision, the individual considers only the asset’s expected return. · What matters, in terms of risk is the covariance of the return to asset with the marginal utility of consumption. In particular a negative covariance increases the demand for asset . Suppose that the individual is given an opportunity to buy a new asset whose expected return equals the rate of return on a risk free asset that the individual is already able to buy. If the payoff to the new asset is typically high when the marginal utility of consumption is high (that is, when consumption is low), that is, , then buy one unit of the asset raised expected utility by more than buying one unit of risk free asset does, the individual can raise his or her expected utility by buying the new asset. · As the individual invests more in the asset, his or her consumption comes to depend more on the asset’s payoff, and so becomes less negative. In the example we are considering, since the asset’s expected return equals the risk free rate, the individual invests in the asset untill · Hedging risks i